Thread View: sci.math.num-analysis
2 messages
2 total messages
Started by Paul Bruckman
Wed, 09 Sep 1998 00:00
Goldbach's Conjecture
Author: Paul Bruckman
Date: Wed, 09 Sep 1998 00:00
Date: Wed, 09 Sep 1998 00:00
10 lines
1556 bytes
1556 bytes
It seems to me that the natural tool that might be used to prove Goldbach's Conjecture is the square of the series of x^p, where the powers are the odd primes. This produces a series of terms A(n)* x^2n, going from n=3 to inf. , and GC would then be equivalent to proving that A(n) > 0 for all such n. Of course, A(n) is odd iff n is prime, corresponding to the representation 2n = n+n, which can only occur in one way, whereas all other representations of 2n occur in pairs. Has anyone thought about this approach, and if so, does anyone see any kind of revelation that might prove A(n)>0 for all n? Paul Bruckman
Re: Goldbach's Conjecture
Author: Felipe Voloch
Date: Thu, 10 Sep 1998 00:00
Date: Thu, 10 Sep 1998 00:00
19 lines
1791 bytes
1791 bytes
Paul Bruckman (aardwolf@gte.net) wrote: : It seems to me that the natural tool that might be used to prove : Goldbach's Conjecture is the square of the series of x^p, where the : powers are the odd primes. This produces a series of terms A(n)* x^2n, : going from n=3 to inf. , and GC would then be equivalent to proving that : A(n) > 0 for all such n. Of course, A(n) is odd iff n is prime, : corresponding to the representation 2n = n+n, which can only occur in : one way, whereas all other representations of 2n occur in pairs. : : Has anyone thought about this approach, and if so, does anyone see any : kind of revelation that might prove A(n)>0 for all n? Paul Bruckman : This is the first step in the Hardy-Littlewood method. The next step is to write A(n) as an integral, using Cauchy's formula. Then the fun starts... Felipe
Thread Navigation
This is a paginated view of messages in the thread with full content displayed inline.
Messages are displayed in chronological order, with the original post highlighted in green.
Use pagination controls to navigate through all messages in large threads.
Back to All Threads